In this work the $B\bar{ B}^*/D\bar{ D}^*$ system is studied in the Bethe-Salpeter approach with quasipotential approximation. In our calculation both direct and cross diagrams are included in the one-boson-exchange potential. The numerical results indicate the existence of a isoscalar bound state $D\bar{ D}^*$ with $J^{ PC}=1^{ ++}$, which may be related to the $X(3872)$. In the isovector sector, no bound state is produced from the interactions of $D\bar{ D}^*$ and $B\bar{ B}^*$, which suggests the molecular state explanations for $Z_b(10610)$ and $Z_c(3900)$ are excluded.
Categories: hep-ph nucl-th